We　formulate　an　epidemic　model　with　age　of　vaccination　and　generalized　nonlinear　incidence　rate,　where　the　total　population　consists　of　the　susceptible,　the　vaccinated,　the　infected　and　the　removed.　We　then　reach　a　stochastic　SVIR　model　when　the　fluctuation　is　introduced　into　the　transmission　rate.　By　using　Itô’s　formula　and　Lyapunov　methods,　we　first　show　that　the　stochastic　epidemic　model　admits　a　unique　global　positive　solution　with　the　positive　initial　value.　We　then　obtain　the　sufficient　conditions　of　the　stochastic　epidemic　model.　Moreover,　the　threshold　tells　the　disease　spreads　or　not　is　derived.　If　the　intensity　of　the　white　noise　is　small　enough　and　R˜00＞1,　then　the　disease　is　weakly　permanent.　The　persistence　in　the　mean　of　the　infected　is　also　obtained　when　the　indicator　Rˆ0＞1,　which　means　the　disease　will　prevail　in　a　long　run.　As　a　consequence,　several　illustrative　examples　are　separately　carried　out　with　numerical　simulations　to　support　the　main　results　of　this　paper.　©　2018